Analytical Chemistry

Quantitative Chemical Analysis

Analytical Chemistry deals with methods fordetermining the chemical composition ofsamples.

• Qualitative Analysis (identification)provides information about the identity ofspecies or functional groups in the sample(an analyte can be identified).

• Quantitative Analysis provides numericalinformation of analyte (quantitate theexact amount or concentration).

Qualitative analysis is what.

Quantitative analysis is how much.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

GOALS OF QUANTITATIVE CHEMICAL ANALYSIS

Involves the determination of the mass ratioof the components in a given sample

Involves the determination of compoundsformula including structural one.

Involves the determination of the quality of amedicinal compound

Classical quantitative analysis uses

mass volume

or physical-chemical changes

to quantify amount

Classifying Quantitative Analytical Methods

• Gravimetric Methods: Determine the mass of the analyte orsome compound chemically related to it. Analyte: the compoundor species to be analyzed in a sample

• Volumetric Methods: The volume of a solution containingsufficient reagent to react completely with the analyte ismeasured.

• Physical-chemical Methods:

A) Spectroscopic Methods: Based on measurement of theinteraction between electromagnetic radiation andanalyte atoms or molecules.

B) Electroanalytical Methods: Involve the measurement ofelectrical properties such as voltage, current,resistance and quantity of electrical charge.

Etc…

The sample size dictates what measurement techniques can be used.

Gravimetric Analysis

gravi – metric(weighing - measure)

Gravimetric Analysis

The Gravimetric analysis is a method of thequantitative chemical analysis which is based on exactmeasurement of weight of defined substance or itscomponents allocated in chemically pure compound orin the form of corresponding compounds

Gravimetric methods:

1) Particulate gravimetry,2) Volatilization gravimetry,3)Precipitation gravimetry.

m - mass

%;100)(

)%( a

ashmash

а – mass of a sample

In some situations, the analyte is already present as in aparticulate form that is easy to separate from its liquid, gas, orsolid matrix. When such a separation is possible, we can applyparticulate gravimetry determine the analyte‟s mass without relyingon a chemical reaction.

The volatilization gravimetry is a method of thegravimetric analysis which is based on measurement ofexact weight of volatile defined component.Volatilization methods: in this the analyte or itsdecomposition products are volatilized at a suitabletemperature or after a chemical reaction. The volatileproduct is then collected and weighed, or, alternatively,the mass of the product is determined indirectly fromthe loss in mass of the sample.

•Direct method of volatilization gravimetry

•Indirect method of volatilization gravimetry

Direct method of volatilization gravimetry. A definedvolatile component is absorbed by a specific absorberand on increase of the weight of the last we cancalculate the weight of a volatile defined component.

%;100)%( 12

a

mmA

m1 – mass of the absorber before the experiment

m2 – mass of the absorber after the experiment

HCl

Na2CO3

CO2

absorber(CaO+NaOH)

а – mass of a sample

Ex. OHCONaClHClCONa 2232

Indirect method volatilization gravimetry. In indirectmethods we can define weight of the rest of substanceafter full removal of a defined volatile component. It isused for moisture determination or to find water ofcrystallization, etc.

%;100)%( 21

a

mmA

m1 – mass of the sample before drying

m2 – mass of the sample after drying

а – mass of a sample

BaCl2∙2H2O (solid) Ct

BaCl2 (solid) + 2H2O (gas)

)(100

100)(

2OH

AA

Analytical laboratories routinely report data on a wet-weightbasis (ω(A)). If requested, the laboratory can report thepercent moisture of the sample so that the results can beconverted to a dry-weight basis (ω„(A)) if desired or required.

The initial concentration, for example mass percent, measuredby the laboratory is considered an "as-is" or "wet" basis result,because no calculations have been made to compensate for themoisture content of the sample. When a "dry" value is reported,the laboratory has measured the moisture content of the sample,and calculated the concentration based on the percent solidspresent in the sample.

"dry" versus "as-is" or "wet"

Precipitation methods: in this method the analyte isconverted to a sparingly soluble precipitate. This precipitate isthen filtered, washed free of impurities, and converted to aproduct of known composition by suitable heat treatment, andthe product is weighed.

Precipitation gravimetry

Gravimetric analysis is one of themost accurate and precise methodsof macroquantitative analysis.

The analyte is selectively converted into an insoluble form(precipitate form).

The separated precipitate is then dried or ignited, possibly toanother form (gravimetric or weighed form) and is accuratelyweighed.From the weight of the precipitate and knowledge of its chemicalcomposition, we can calculate the weight of the analyte in thedesired form.

Key steps in aprecipitation reaction-what this looks like

Weighing the sample

Forming a precipitate

Filtering the solution

Weighing thedry precipitate

Example: Determination of sodium suphate

Scheme of analysis:

44

)(

422 BaSOBaSOSONa

otexcessBaCl

Defined substance Precipitating formGravimetric or Weighed form

Precipitating agent

CALCULATIONS IN GRAVIMETRY

SCHEME OF ANALYSIS:

44

)(

422 BaSOBaSOSONa

otexcessBaCl

Defined compound orAnalyte

Precipitating form Gravimetric or weighed form

Precipitation agent

)()( 442 BaSOnSONan

)(

)(

)(

)(

4

4

42

42

BaSOM

BaSOm

SONaM

SONam

)(

)()()(

4

42442

BaSOM

SONaMBaSOmSONam

)(

)(

4

42

BaSOM

SONaMF

FBaSOmSONam )()( 442

The gravimetric factor shows a part of a definedcomponent into the weighed (gravimetric) form.

)(

)(

formweighedM

compounddefindMF

Fformweighedmcompounddefindm )()(

Fundamental formula of precipitation gravimetry

323

),(

4 )(22 223 OFeOHFeFeSOotOHexcessNH

Defined substance Precipitating form Gravimetric or Weighed form

Precipitating agent

FOFemOFeM

FeSOMOFemFeSOm )(

)(

)(2)()( 32

32

4324

In many cases, the weighed form of theprecipitate can be different from theprecipitated form.

Sampling

Preparation of the solution

Precipitation

Filtration и Washing

Drying or Igniting

Weighing

Calculation

THE MAIN OPERATIONS OF A PRECIPITATION GRAVIMETRY ARE THE SUCH:

•A drug analyst often has to determine the characteristics of alarge quantity of drug material, such as the contents of a batcharriving at a pharmacy, a days worth of production, or theproducts stored in a warehouse. Ideally, the analyst would liketo analyze every part of the material to obtain an accuratemeasure of the property of interest, but in most cases this ispractically impossible. Many analytical techniques destroy themedicine and so there would be nothing left to sell if it were allanalyzed.• Another problem is that many analytical techniques are timeconsuming, expensive or labor intensive and so it is noteconomically feasible to analyze large amounts of material. It istherefore normal practice to select a fraction of the wholematerial for analysis, and to assume that its properties arerepresentative of the whole material.�•Selection of an appropriate fraction of the whole material isone of the most important stages of medicine analysisprocedures, and can lead to large errors when not carried outcorrectly.�

Sampling

It is convenient to define some terms used to describe thecharacteristics of a material whose properties are going to beanalyzed.�� Population.� The whole of the material whoseproperties we are trying to obtain an estimate of is usuallyreferred to as the �population�.� Sample. Only a fraction of the population is usuallyselected for analysis, which is referred to asthe �sample.� The sample may be comprised of one ormore sub-samples selected from different regions within thepopulation.� Laboratory Sample.� The sample may be too large toconveniently analyze using a laboratory procedure and so only afraction of it is actually used in the final laboratory analysis.This fraction is usually referred to as the �laboratorysample�.�

Sampling

The primary objective of sample selection is to ensure that theproperties of the laboratory sample are representative of theproperties of the population, otherwise erroneous results will beobtained.� Selection of a limited number of samples foranalysis is of great benefit because it allows a reduction intime, expense and personnel required to carry out the analyticalprocedure, while still providing useful information about theproperties of the population. Nevertheless, one must always beaware that analysis of a limited number of samples can only givean estimate of the true value of the whole population. Once wehave selected a sample that represents the properties of thewhole population, we must prepare it for analysis in thelaboratory. The preparation of a sample for analysis must bedone very carefully in order to make accurate and precisemeasurements.

Selected and weighed sample is transferred to a beakervolume of 250-300 ml and dissolved in distilled water. Insolublein water sample, usually dissolved in acids.

Preparation of the solution

Precipitation gravimetric analysis usually involvesprecipitation of analyte from solution.

This may require:

- to chose a proper precipitation agent (precipitant) - to calculate quantity of a precipitant - to respect conditions of precipitation - complete precipitation

Precipitation

the most important operation

The ideal product (precipitate) of a gravimetric analysis shouldbe:

•Sufficiently insoluble (Ksp10-8) (the precipitate is of such low

solubility that losses from dissolution are negligible)

•Easily filterable (crystals of large particle size so as not topass through the filtering system).

•Very pure (less possibility that the precipitates carry some ofthe other constituents of the solution with them).

•The precipitate‟s form should turn easily enough in weighed(gravimetric) form.

Properties of the Precipitate Form

Which of the following is the best substance that canbe chosen for use as a precipitate in a gravimetricanalysis of calcium?

А. СaSO4 (Ksp = 2,5·10-5)

В. СaСO3 (Ksp = 3,8·10-9)

С. СaС2O4 (Ksp = 2,3·10-9)

D. СaСrO4 (Ksp = 7,1·10-4)

E. СaF2 (Ksp = 4,0·10-11)

lmolKS spCaSO /100,5105,2 35

4

lmolKS spCaCO /102,6108,3 59

3

lmolKS spOCaC /108,4103,2 59

42

lmolKS spCaCrO /107,3101,7 24

4

lmolS spK

CaF /102,2 434

100,434

11

2

Test

Chose the best reagent for precipitating Ca2+ ions in a gravimetricanalysis

А. Na2C2O4

В. K2С2O4

С. H2С2O4

D. (NH4)2С2O4

E. Li2С2O4

Properties of the Precipitation Agent

1. It is desirable, that a precipitant was volatilecompound.

Test

How to chose a proper precipitant?

2. A precipitant should be specific – to precipitate a defined ion in the presence of others ions.

Example,Al3+, Cr3+

NH3Al(OH)3

Organic precipitants

• dimethylgloxime• 8-oksihinolin • oxalic acid• -nitrozo--naphtol

Inorganic precipitants

• Alkalis or ammonia• Hydrogene sulphide or

sulphides• Sulphatic acid• Phosphatic acid

Advantage of organic precipitants consists in the following:

•Solubility of precipitate with organic precipitants isless.

• Precipitates with organic reagents are crystal.

•Precipitates with organic reagents are purer as ontheir surface impurity are less adsorbed.

•Organic precipitant have higher selectivity andspecificity.

•The gravimetric factor at definition with organicreagents on much less so, accuracy of definitionincreases.

In the gravimetric analysis a precipitation isconsidered practically full if in a solution definedsubstance is in limits of accuracy of weighing it isless than 0,0002-0,0001 g

Take a volatile precipitant in 2-3 times more thancalculated quantities (count on the reaction equation)

Take a nonvolatile precipitant in 1,5 times more thancalculated quantities (count on the reaction equation)

Calculation of quantity of precipitant

Favorable conditions for precipitation

The constituents of a precipitate can be arranged in twogeneral ways: they can form a regular repeating three-dimensional structure called a crystal lattice, thus producinga crystalline precipitate, or they can aggregate with noparticular order, in which case they form an amorphousprecipitate (from the Greek ámorphos, meaning “shapeless”).

Precipitates made up of large particles are generallydesirable in gravimetric work because large particles areeasy to filter and wash free of impurities. In addition,such precipitates are usually purer than are precipitatesmade up of fine particles.

a) Conditions of precipitation of crystal precipitates:

1. A precipitation are carried from enough diluted solutions by the dilutedsolution of precipitant.

2. Add a precipitant very slowly, on drops.

3. A solution are mixed continuously by a glass stick to avoid strong localsatiation at addition of precipitant.

4. Conduct precipitation from a hot solution, and sometimes heat up also asolution of precipitant (to increase solubility).

5. Filter a precipitate only after cooling of solution. Digestion of crystallineprecipitates (without stirring) for some time after formation frequentlyyields a purer, more filterable product.

The precipitate is left hot (below boiling) for 30 min to 1hour in order for the particles to be digested. Digestioninvolves dissolution of small particles and reprecipitation onlarger ones resulting in particle growth and betterprecipitate characteristics.

During digestion at elevated temperature:

1.Small particles tend to dissolve and reprecipitate onlarger ones.2.Individual particles agglomerate.3.Adsorbed impurities tend to go into solution.

Digestion

Digestion is keeping the precipitate formed in contact with themother liquor for a specified amount of time. Mother liquor(the solution from which it was precipitated).

1. A precipitation conduct from the concentrated solutions bythe concentrated solutions of precipitant.

2. A precipitation conduct from hot solutions.

3. A precipitation conduct in the presence of electrolyte -coagulant.

4. A precipitate quickly filter and do not leave under a matrixsolution.

b) Conditions of precipitation of amorphous precipitates:

Avoiding Impurities

Precipitation gravimetry is based on a knownstoichiometry between the analyte‟s mass and themass of a precipitate. It follows, therefore, thatthe precipitate must be free from impurities.Since precipitation typically occurs in a solutionrich in dissolved solids, the initial precipitate isoften impure. Any impurities present in theprecipitate‟s matrix must be removed beforeobtaining its weight.

Coprecipitation is the phenomenon in whichsoluble compounds are removed from solutionduring precipitate formation.

There are three types of coprecipitation: 1. occlusion,2. isomorphous replacement,3. surface adsorption,

Impurities encountered in Gravimetric Analysis

•1. OCCLUSION

•This occurs when materials that are not part of thecrystal structure are trapped within the crystal.

•For example, water or any counter ion can beoccluded in any precipitate.

•This causes deformation in the crystal.

•This type is hard to be removed, digestion candecrease it to a certain extent.

•2. ISOMORPHOUS REPLACEMENT (INCLUSION)

•This occurs when a compound that is isomorphous to theprecipitate is entrapped within the crystal.

•Isomorphous means they have the same type of formula andcrystals in similar geometric form.

•This type of impurity doesn‟t lead to deformation of thecrystals.•Example, K+ has nearly the same size of NH4

+ so it can replaceit in Magnesium ammonium phosphate.•Digestion cannot handle this type and mixed crystals will beformed.

3. SURFACE ADSORPTION

•Surface adsorption is very common especially in colloidal precipitates.•Example, AgCl, BaSO4, where each of them will have a primary adsorption layer of the lattice ion present in excess followed by a secondary layer of the counter ion of opposite charge.•These adsorbed layers can often be removed by washing where they can be replaced by ions that can be easily volatilized at the high temperature of drying or ignition.

4. POST PRECIPITATION

•When the precipitate is allowed to stand incontact with the mother liquor, a second substancewill slowly form a precipitate on the surface ofthe original one.

•Examples, When calcium oxalate is precipitated inthe presence of magnesium ions, magnesiumoxalate may be if the solution is left withoutfiltration for a long time.

•Digestion will increase the extent of such type,dissolution and reprecipitation will decrease theextent of post precipitation.

• Paper‟s filters (weight of ashes 0,00003 –0,00007 g)

• Glass filters or filtering crucibles.

Filtering

Proper procedure for filtering solids using filterpaper. The filter paper circle in (a) is folded in half(b), and folded in half again (c). The filter paper isparted (d), and a small corner is torn off (e). Thefilter paper is opened up into a cone and placed in thefunnel (f). Note that the torn corner is placed to theoutside.

Rinsing the precipitate

• Rinsing on the filter (foramorphous precipitate)

• Rinsing by decantation (forcrystal precipitate)

Procedure for filtering through a filtering crucible.The trap is used to prevent water from a wateraspirator from backwashing into the suction flask.

Washing the PrecipitateIt is crucial to wash the precipitate very well in

order to remove all adsorbed species which willadd to weight of precipitate. One should becareful not to use too much water since part ofthe precipitate may be lost. Also, in case ofcolloidal precipitates we should not use water asa washing solution since peptization would occur.In such situations dilute nitric acid, ammoniumnitrate, or dilute acetic acid may be used.Usually, it is a good practice to check for thepresence of precipitating agent in the filtrate ofthe final washing solution. The presence ofprecipitating agent means that extra washing isrequired.

• Crystal precipitates with low solubilityare rinsed by water

• Amorphous precipitates are rinsed bysolutions of volatile electrolytes toavoid of peptization of a precipitate

• Precipitates with high solubility arerinsed by solutions of electrolytes whichcontain the same ion with a precipitate

Choice of a rinsing liquid

Drying or Ignition

After filtration, a gravimetric precipitate is heateduntil its mass becomes constant.

Drying at 110 to 120 °C for 1-2 hours is conducted ifthe collected precipitate is in a form suitable forweighing (known, stable composition), it must be heatedto remove water and to remove adsorbed electrolytefrom the wash liquid. Heating removes the solvent andany volatile species carried down with the precipitate.

Ignition (strong heating) at much higher temperatureis usually required if a precipitate must be convertedto a more suitable form for weighing.

Some precipitates are also ignited to decompose thesolid and form a compound of known composition. Thisnew compound is often called the weighing form.

The temperature required to produce a suitableweighing form varies from precipitate to precipitate.

• Exact conformity of structure to the chemicalformula

• Chemical stableness of the weighed form.Unreactive with constituents of the atmosphere

•The contents of a defined element in the weighedform should be as it is possible smaller.

•It is desirable that a gravimetric (weighed) formhas a large molecular mass

Properties of the Gravimetric (Weighed) Form

Which of the following is the best substance that canbe chosen for use as a weighed form in a gravimetricanalysis of zinc?

А. ZnO (Mr = 81,37)

В. NaZn(UO2)3·(C2H3O2)9·6H2O (Mr = 1537)

С. Zn2P2O7 (Mr = 304,72)

D. ZnSO4 (Mr = 161,43)

E. ZnS (Mr = 97,45)

Test

!!! Drying of weighed form are leadedto its constant weight, that is thedifference between its parallelweighing will not exceed 0,0002 g

The crucibles first cleanedthoroughly and then subjected tothe same regimen of heating andcooling as that required for theprecipitate.This process is repeated untilconstant mass has been achieved,that is, until consecutive weighingdiffer by 0.3 mg or less.

Drying in porcelain and glass filtering crucibles

•After the precipitate is allowed to cool(preferably in a desiccator to keep it fromabsorbing moisture), it is weighed (in the crucible).

•Properly calibrated analytical balance

•Good weighing technique

Weighing

Advantages and Disadvantages of thegravimetric analysis

Advantages

1. High accuracy (0,005-0,1 %)

2. High reproducibility

3. Simplicity of performance

Disadvantages

1. Duration

2. Labour input

•Determination of moisture in drugs (indirectvolatilization gravimetry).

•

Determination of water (direct volatilizationgravimetry).

•

Determination of the dry rest in extracts, tinctures(indirect volatilization gravimetry).

•

Determination of sulphatic ashes and ashes(particulate gravimetry).

•

Determination of drugs (precipitation and particulategravimetry).

USE GRAVIMETRY IN THE PHARMACEUTICAL ANALYSIS

ERRORS AND STATISTICS

Classification of errors

Errors are of three main types:

•Systematic (Determinate) errors

• Random (Indeterminate) errors

• Gross errors

Systematic (Determinate) errors

These are errors which can be avoided ifcare is taken, whose magnitude can bedetermined. Systematic errors are classifiedinto three types:

Instrumental error

Methodic error

Operative error

Instrumental errors

Instrumental errors are introduced due to

•the use of defective instruments, the faulty constructions ofbalances, uncalibrated or improperly calibrated weights,graduated glassware.

For example, an error in volumetric analysis will beintroduced when a 20 ml pipette, which actually measures 20,1ml, is used

•sometimes an instrument error may arise from the environmentalfactors on the instrument.

For example, a pipette calibrated at 20 C, if used at 30Cwill introduce error in volume

•the use of reagents containing impurities

Instrumental errors may largely be eliminated by periodicalcalibrating the instruments.

Operative errors

These errors are also called personalerrors and are introduced because ofvariation of personal judgments

For example, due to colour blindness aperson may arrive at wrong results in avolumetric analysis.

Using incorrect mathematical equation andcommitting arithmetic mistakes will alsocause operative errors.

Methodic errors

These errors are caused by adoptingdefective experimental methods.For example in volumetric analysis the useof an improper indicator leading to wrongresults is an example for methodic error.Proper understanding of the theoreticalbackground of the experiments is anecessity for avoiding methodic errors.

Random (Indeterminate) errors

These errors are also called accidental errors. Indeterminateerrors arise from uncertainties in a measurement that areunknown and which cannot be controlled by the experimentalist.

For example, when pippeting out a liquid, the speed of draining,the angle of holding the pipette, the portion at which the pipetteis held, etc, would introduce indeterminate error in the volume ofthe liquid pipette out.

If a large number of measurements are taken, the resultsattained will usually be distributed about the mean in a roughlysymmetrical manner. The mathematical model that bestsatisfies such a distribution of random errors is called a Normal(or Gaussian) distribution. This is a curve that is symmetricalabout the mean as shown in Fig. An inspection of this errorcurve shows:a) Small errors occur more frequently than large onceb) Positive and negative errors of the same numerical magnitude

are equally likely to occur

defined value

prob

ability

Gross errors are caused by experimentercarelessness or equipment failure. These"outliers" are so far above or below the truevalue that they are usually discarded whenassessing data.

Gross errors

Tests

1. Select systematic errors:

A. Errors caused by out of order balance;

B. Errors produced by an unknown cause;

C. Errors produced by inaccurate volume reading from a

burette;

D. Errors due to the use of impure chemicals;

E. Errors due to the use of a solution with incorrect determined

concentration.

2. Which of the following errors are not systematic?

A. Errors caused by mis-calibration of a balance;

B. Errors caused by no compliance of some conditions of

analysis;

C. Errors produced by an unknown cause;

D. Errors due to carelessness during the analysis;

E. Errors due to the incorrect choice of the analysis

method.

3. Select correct statements:

A. A random error is the error that fluctuate arbitrarily after

repeated measurements;

B. The error that remain constant after repeated measurements

is named a gross error;

C. Random errors can be positively identified and have a definite

measurable value;

D. Random errors cannot be positively identified and do not have

a definite measurable value;

E. In case of random errors repeated measurements yield results

that fluctuate above and below the true value.

MEAN VALUE

A mean value is obtained by dividing the sum of a setof replicate measurements by the number of individualresults in the set.

For example, if a gravimetric analysis is repeatedthree times and the mass values are 0,1345 g,0,1355 g and 0,1349 g

1349,03

4040,0

3

1349,01355,01345,0

Mean

This mean value is also called arithmetic mean or average

ACCURACY

represents the nearness to a measurement to itsexpected value. Any difference between the measuredvalue and the expected value is expressed as error.

For example:

The concentration of NaCl in physiologic sodium chloridesolution is 0,90%. In an experiment, if a student arrives atexactly this value, his value is said to be accurate.

PRECISION (REPRODUCIBILITY)

Precision is defined as the agreement between thenumerical value of two or more measurements of thesame object that have been made in an identicalmanner. Thus, a value is said to be precise, whenthere is agreement between a set of results for thesame quantity.

However a precise value need to be accurate.

Methods of expressing precision

Precision can be expressed in an absolute method. In the absolute way the deviation from the mean │Xi -X│ express precision without considering sign

Nr Sample Mass of the defined

component (g)

Deviation from

mean

│Xi -X│

1 X1 0,1345 0,0005

2 X2 0,1355 0,0005

3 X3 0,1349 0,0001

X = 0,1350 0,0011/3 = 0,0004average deviation

A small average deviation indicates data points clustered closely around themean and good precision.

ABSOLUTE ERROR

The term accuracy is denoted in terms of absolute errorEa.

Ea is the difference between the observed value (Xi)and the expected value (A) (or mean value (X)).

Example

If a student obtains a value of 0,93% for the concentration of physiologic sodium chloride solution, the absolute error in this determination is :

Ea = 0,93 – 0,90 = 0,03

Ea = X – A =Хi – X

X – observed valueА – expected value

RELATIVE ERROR

Sometimes the term relative error is used to expressthe uncertainty in data. The relative error denotesthe percentage of error compared to the expectedvalue. For the concentration of physiological solutionreported.

%33,3%10090,0

03,0 rE

%100X

E

raE %100

A

E

raEor

.

Test

Select correct statements:

A. Absolute error is the difference between a measured value

and an actual value;

B. Absolute error is the difference between a measured value

and mean value;

C. Accidental errors are produced by permanent causes;

D. Accidental errors are produced by known causes;

E. Relative error is the ratio of an actual value to absolute

error

Select correct statements:

A. Systematic errors are produced by unknown causes;

B. Accidental errors are produced by known causes;

C. Relative error is the ratio of absolute error to an actual

value of a measurement being taken;

D. Relative error is the ratio of absolute error to a mean

value of a measurement being taken;

E. Mis-calibration of a balance can lead to a gross error.

Problem

A sample of NH4Fe(SO4)2 weighing 2,7165 g was dissolved in 500 ml ofwater. A 20,00 ml of the prepared solution was treated to produce0,3588 g of a precipitate of BaSO4. calculate mass percent (%) of Fein the original sample.

Solution:

4244 )( BaSOFeSOFeNHDefined compound Gravimetric or

weighed formAnalyte

2

)(2

)()()()(

4

44BaSOM

FeMBaSOmFBaSOmFem

gFem 0429,039,2332

85,553588,0)(

0,0429 20 mL

Х 500 mL

gX 0725,120

0429,0500

%48,39%1007165,2

0725,1)%( Femass

Problem

A sample of a mixture containing K2CO3 and KHCO3 weighed 1,712 g.This sample was heated to form carbon bioxide. If 0,5512 g of CO2

were formed from the heating of the mixtur, what is the percentage ofK2CO3 and KHCO3 in a sample.

Solution:

K2CO3

KHCO3 CO2

CO2

m = 0,5512 gа = 1,712 g

m(CO2 )= m1(CO2 ) +m2(CO2 ) =0,5512 г

Х

1,71 - Х

m(К2CO3 )= Х m(КНCO3 )= 1,712 - Х

)(1364,344

21,138)(

)(

)()()()( 2121

2

32212132 COmCOm

COM

COKMCOmFCOmCOKm

)(2752,244

11,100)(

)(

)()()()( 2222

2

322223 COmCOm

COM

KHCOMCOmFCOmKHCOm

Let‟s write gravimetric formula for each component of the mixture:

)(1364,3 21 COmX

)(2752,2712,1 22 COmX

Using abbreviations introduced above, we can write

1364,3)( 21

XCOm

2752,2

712,1)( 22

XCOm

5512,02752,2

712,1

1364,3)()( 2221

XXCOmCOm

5512,0)712,1(4395,03188,0 XX

gX 6678,1

m(К2CO3 )= Х =1,6678 g

m(КНCO3 )= 1,712 – Х = 0,0442 g

%42,97%100712,1

6678,1)%( 32 COKmass

%58,2%100712,1

0442,0)%( 3 KHCOmass